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why dont you stay up both nights shavuos, because it is difficult, so also on pesach at least stay up two nights.
if the problem is the wine, why have wine that makes you sleepy. have low alcohol dry wine.
wolfish musings
who says sleeping first is not properly observing the minhag, the reason for the minhag is to be awake early in the morning, not to be awake the whole night.